Upgrading from:

Geometry`Polytopes`

Geometry`Polytopes` functionality is available in the kernel function PolyhedronData.

Get the vertex coordinates of an octahedron:

Version 5.2 << Geometry`Polytopes`;
Vertices[Octahedron]

Get the Schläfli symbol:

Version 5.2 << Geometry`Polytopes`;
Schlafli[Octahedron]

Area, CircumscribedRadius, Dual, Faces, InscribedRadius, NumberOfEdges, NumberOfVertices, NumberOfFaces, and Volume were available in previous versions of Mathematica and are now available on the web at library.wolfram.com/infocenter/MathSource/6828.